The invention relates to a method and an apparatus for enhancing the probability of substantially error-free reception of a signal consisting of a sequence of discrete bits with the aid of a threshold comparison. Digital signals, such as binary signals, are usually processed with the aid of a constant threshold value. If the received signal is equal or exceeds a given threshold value, then the received signal is assigned a logical value of "1". If the received signal is, however, smaller than the threshold value, then the received signal is assigned a value of a logical "0". If the received signal is contaminated as the result of interfering signals and distortions in the transmission channel, then the aforenoted method may lead to erroneous and impermissible results. To avoid such disadvantageous results, the received and deformed signal must be corrected for distortion. From Mese et al, U.S. Pat. No. 4,109,211 there is known a method of slow threshold adaption, which permits the receiver to make an automatic adjustment over a long period of time independent of any changes in the received signal, which are conditioned by slow changes of the transmission conditions of the channel.